On the eccentricity inertia indices of chain graphs

Jing Huang and Minjie Zhang

Applied Mathematics and Computation, 2025, vol. 493, issue C

Abstract: For a given graph G, the eccentricity matrix of it, written as ε(G), is created by retaining the largest non-zero entries for each row and column of the distance matrix, while filling the rest with zeros, i.e.,ε(G)uv={d(u,v),ifd(u,v)=min⁡{ε(u),ε(v)},0,otherwise, where ε(u) denotes the eccentricity of a vertex u. The eccentricity inertia index of a graph G is represented by a triple (n+(ε(G)), n0(ε(G)), n−(ε(G))), where n+(ε(G)) (resp., n0(ε(G)),n−(ε(G))) is the count of positive (resp., zero, negative) eigenvalues of ε(G). In this paper, for each chain graph (a graph which does not contain C3,C5, or 2K2 as induced subgraphs), the eccentricity inertia index of it is completely determined.

Keywords: Chain graph; Eccentricity inertia index; Quotient matrix (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:493:y:2025:i:c:s009630032400732x

DOI: 10.1016/j.amc.2024.129271

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